This page gathers the 457 dictionary entries belonging to the domain “Logic”, as labelled by Wiktionary. Each word leads to its full entry: definitions, etymology, pronunciation, examples. Page 1 of 5: from “a” to “contraposition”.
- a symbol A universal affirmative suggestion.
- a fortiori adj With stronger or greater reason; as a corollary implied by a stronger claim; even more so; all the more so; so much the more.
- a posteriori adj Involving induction of theories from facts.
- a priori adv In a way based on theoretical deduction rather than empirical observation.
- abdicative noun A reasoning from the negative
- abduction noun A syllogism or form of argument in which the major premise is evident, but the minor is only probable.
- abductive adj Being or relating to a logical process of abduction or inference.
- abjunction noun Synonym of material nonimplication.
- accentus noun Ambiguity arising when the meaning of a sentence is changed by placing an unusual prosodic stress, or when, in a written passage, it is…
- accidens noun Synonym of accident (“a property, fact, or relation that is the result of chance or is nonessential or nonsubstantive”).
- adicity noun The number of arguments or operands a function or operation takes. For a relation, the number of domains in the corresponding Cartesian…
- adjunctive adj The property of two operations x and y, such that ax(ayb) = a, and ay(axb) = a.
- affirmative adj Expressing the agreement of the two terms of a proposition.
- affirming the consequent noun A formal fallacy, committed by reasoning in the form
- alethic adj Of or pertaining to the various modalities of truth, such as the possibility or impossibility of something being true.
- alternation noun The "inclusive or" truth function.
- analogism noun An argument from cause to effect; an a priori argument.
- analysis noun Proof by deduction from known truths.
- analytic adj that follows necessarily by definition; tautologous.
- ancestral noun A relationship in which something is a precursor.
- and verb To combine (a value) with another value by means of this operator.
- Andersonian adj Of or pertaining to Alan Ross Anderson (1925–1973), American logician, or his work in relevance logic and deontic logic.
- antecedent noun The conditional part of a hypothetical proposition, i.e. p→q, where p is the antecedent, and q is the consequent.
- antepredicament noun A prerequisite to a clear understanding of the predicaments and categories, such as definitions of common terms.
- antinomy noun In the thought of the German philosopher Immanuel Kant (1724–1804): an apparent contradiction between valid conclusions; a paradox.
- apagoge noun An indirect argument which proves a thing by showing the impossibility or absurdity of the contrary.
- apodeictic adj Of the characteristic feature of a proposition that is necessary (or impossible): perfectly certain (or inconceivable) or incontrovertibly…
- argument noun A series of propositions organized so that the final proposition is a conclusion which is intended to follow logically from the preceding…
- argument form noun The result of replacing parts of an argument with letters, leaving only logic words such as "if" and "for all" unreplaced.
- argument instance noun The argument resulting when the blanks of an argument form are filled in with specific terms or statements.
- arithmetical hierarchy noun A hierarchy which classifies the complexity of first-order formulae (and sets defined by them) based on the number of alternations between…
- arity noun The number of arguments or operands a function or operation takes. For a relation, the number of domains in the corresponding Cartesian…
- association fallacy noun a formal fallacy that asserts that properties of one thing must also be properties of another thing if both things belong to the same group
- assumption noun The minor or second proposition in a categorical syllogism.
- atomic adj Lacking logical operators; unable to be made simpler in logical form.
- attribute noun That which is predicated or affirmed of a subject; a predicate; an accident.
- axiom noun A fundamental assumption that serves as a basis for deduction of theorems; a postulate (sometimes distinguished from postulates as being…
- axiom schema noun A formula in the language of an axiomatic system, in which one or more schematic variables appear, which stand for any term or subformula…
- axiom scheme noun A formula in the language of an axiomatic system, in which one or more schematic variables appear, which stand for any term or subformula…
- beg the question verb To engage in the logical fallacy of begging the question (petitio principii).
- biconditional noun An "if and only if" conditional wherein the truth of each term depends on the truth of the other
- binary adj Concerning logic whose subject matter concerns such states.
- bisimulation noun an equivalence relation between state transition systems, associating systems which behave in the same way in the sense that one system…
- Boolean noun A variable that can hold a single true/false (1/0) value.
- Boolean algebra noun Specifically, an algebra in which all elements can take only one of two values (typically 0 and 1, or "true" and "false") and are subject…
- Boolean atom noun A logical proposition that cannot be derived from other logical propositions by a Boolean operation.
- Boolean function noun Any function based on the operations AND, OR and NOT, and whose elements are from the domain of Boolean algebra
- bound adj Constrained by a quantifier.
- by extension prep_phrase Used to connect the internal logic of two statements.
- canonical conjunctive normal form noun Conjunctive normal form with the additional property that all of the terms of the product contain the same literals, so that the terms…
- canonical disjunctive normal form noun Disjunctive normal form with the additional property that all of the terms of the sum contain the same literals, so that the terms differ…
- categorical noun A categorical proposition.
- categorical proposition noun A proposition that asserts or denies that members of one category (the subject term) belong to another (the predicate term). There are four…
- cherry-pick verb To select only evidence which supports an argument, and reject or ignore contradictory evidence.
- chicken-or-egg question noun A supposed paradox concerning whether chickens or chicken eggs existed first.
- Church-Rosser property noun The property of a rewriting system for which x stackrel *↔y implies x mathbin ↓y for all objects x, y.
- circle noun A form of argument in which two or more unproved statements are used to prove each other; inconclusive reasoning.
- circular argument noun An argument which commits the logical fallacy of assuming what it is attempting to prove.
- classical logic noun A kind of logic based on the principles that each proposition has a truth value of either "true" or "false", but not both, and that if a…
- closed adj Lacking a free variable.
- closed formula noun A formula which has no free occurrences of variables; or equivalently, in which all occurrences of variables are bound.
- coextensive adj Having the same extension—the object or set of objects to which a term refers.
- coinduction noun A form of induction that allows some form of reasoning concerning sets that are not well founded; uses a form of relation called a…
- coinstance noun A fellow instance (of a theme, concept, etc), which may be a discrete (separate) one or a coinstantiation.
- collectional adj Pertaining to all elements of a collection simultaneously, rather than to the individual elements of the collection or to the collection as…
- colligation noun The formulation of a general hypothesis which seeks to connect two or more facts.
- common knowledge noun A special kind of knowledge for a group of agents, such that when all the agents in a group G know p, they all know that they know p, they…
- comparate noun One of two things being compared.
- complement noun An expression related to some other expression such that it is true under the same conditions that make other false, and vice versa.
- complete adj In which every semantically valid well-formed formula is provable.
- completeness noun The property of a logical theory that whenever a wff is valid then it must also be a theorem. Symbolically, letting T represent a theory…
- completory adj Serving to fulfil or complete (e.g. complete a set).
- comprehension noun The totality of intensions, that is, attributes, characters, marks, properties, or qualities, that the object possesses, or else the…
- computability theory noun Recursion theory.
- conclude verb to deduce, to infer (develop a causal relation)
- conclusion noun In an argument or syllogism, the proposition that follows as a necessary consequence of the premises.
- conclusion indicator noun A word or phrase that signals a conclusion in an argument, such as: therefore, thus, so, hence, consequently, accordingly, for this reason…
- concrete noun A term designating both a quality and the subject in which it exists; a concrete term.
- conditional adj Stating that one sentence is true if another is true.
- conditional proof noun A proof showing that if an assumption A is true then a consequent statement or conclusion B must also be true, i.e. B is true on the…
- conjunct noun Either term of a conjunction.
- conjunction noun The proposition resulting from the combination of two or more propositions using the ∧ ( and ) operator.
- conjunctive noun A conjunction.
- conjunctive normal form noun The form of a Boolean formula that the formula has if the formula is a conjunction of disjunctions of literals, such as “(A or B or C) and…
- connective noun A function that operates on truth values to give another truth value.
- connotation noun The attribute or aggregate of attributes connoted by a term, contrasted with denotation.
- consecution noun The relation of consequent to antecedent.
- consequent noun The second half of a hypothetical proposition; Q, if the form of the proposition is "If P, then Q."
- conservative extension noun An extension of a logical theory such that every theorem expressible in the original theory is also derivable within the original theory.
- consilience noun The concurrence of multiple inductions drawn from different data sets.
- consistency noun Freedom from contradiction; the state of a system of axioms such that none of the propositions deduced from them are mutually contradictory.
- consistent adj Of a set of statements: such that no contradiction logically follows from them.
- constructive logic noun Any kind of logic in which any proof of existence can be converted into an algorithm that constructs the mathematical object which it…
- context noun For a formula: a finite set of variables, which set contains all the free variables in the given formula.
- contingency noun A statement which is neither a tautology nor a contradiction.
- contradiction noun A proposition that is false for all values of its propositional variables or Boolean atoms.
- contradictory noun Either of a pair of propositions, that cannot both be true or both be false.
- contrapose verb To place in contraposition.
- contraposed adj Forming a contraposition.
- contraposition noun The statement of the form "if not Q then not P", given the statement "if P then Q".